A Non-standard Version of the Borsuk-Ulam Theorem

• Autorzy: Carlos Biasi , Denise de Mattos
• Języki publikacji: EN

Abstrakty

EN

E. Pannwitz showed in 1952 that for any n ≥ 2, there exist continuous maps φ:Sⁿ→ Sⁿ and f:Sⁿ→ ℝ² such that f(x) ≠ f(φ(x)) for any x∈ Sⁿ. We prove that, under certain conditions, given continuous maps ψ,φ:X→ X and f:X→ ℝ², although the existence of a point x∈ X such that f(ψ(x)) = f(φ(x)) cannot always be assured, it is possible to establish an interesting relation between the points f(φ ψ(x)), f(φ²(x)) and f(ψ²(x)) when f(φ(x)) ≠ f(ψ(x)) for any x∈ X, and a non-standard version of the Borsuk-Ulam theorem is obtained.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 1
• Strony: 111-119

Daty

wydano

2005

Twórcy

autor

Carlos Biasi

• Departamento de Matemática-ICMC, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos SP, Brazil

autor

Denise de Mattos

• Departamento de Matemática-ICMC, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos SP, Brazil

Identyfikatory

DOI

10.4064/ba53-1-10